Allocation and usage of one Elastic IP addresses per instance is usually free, see the section below for Elastic IP Addresses on Amazon EC2 Pricing:

Example :
Region: US East (N. Virginia)
$0.005 per Elastic IP address not associated with a running instance per hour on a pro rata basis.
$0.00 for one Elastic IP address associated with a running instance.
$0.00 per Elastic IP address remap for the first 100 remaps per month.
$0.005 per additional Elastic IP address associated with a running instance per hour on a pro rata basis.
$0.10 per Elastic IP address remap for additional remaps over 100 per month.

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AMIs that are eligible for the free tier are marked in the Amazon EC2 Launch Wizard as Free tier eligible. The free tier allotment for Linux and Microsoft Windows instances is counted separately. You can run 750 hours of a Linux t2.micro or t1.micro instance plus 750 hours of a Windows t2.micro or t1.micro instance each month for the first 12 months.